Answer:
a). 32000
b).
c). 1259
Step-by-step explanation:
Growth of a bacteria is always exponential. Therefore, population of the bacteria is represented by the the geometric sequence.
Sum of the bacterial population after t hours will be represented by
Where a = population at the start
r = ratio with the population is growing
n = time or duration of the growth in one hour
a). Population of 500 bacteria gets doubled after half an hour.
Or gets 4 times after an hour
This sequence will have a common ratio r = 4
and initial population a = 500
Therefore, population of the bacteria after 3 hours will be
b). After t hours number of bacteria will be represented by
c). We have to calculate the population after 40 minutes.
That means duration 't' = 40 minutes of hours
By the formula,
≈ 1259
Therefore, number of bacteria after 40 minutes will be 1259.
